Question

consider the formula for the average velocity, v, of a moving particle. in the formula, $d_1$ and $d_2$ represent the distance traveled by the particle at times $t_1$ and $t_2$ respectively.
$v=\frac{d_2 - d_1}{t_2 - t_1}$
which of the following equations is equivalent to the formula for velocity?
a. $d_2 = v(t_2 - t_1)+d_1$
b. $d_1 = v(t_2 - t_1)-d_2$
c. $t_1 = v(d_2 - d_1)-t_2$
d. $t_2 = v(d_2 - d_1)+t_1$

Explanation:

Step1: Cross - multiply the velocity formula

Starting with $v=\frac{d_2 - d_1}{t_2 - t_1}$, we get $v(t_2 - t_1)=d_2 - d_1$.

Step2: Isolate $d_2$

Add $d_1$ to both sides of the equation $v(t_2 - t_1)=d_2 - d_1$. So, $d_2=v(t_2 - t_1)+d_1$.

Answer:

A. $d_2 = v(t_2 - t_1)+d_1$